An arc measuring less than 180 degrees is known as a minor arc.
Understanding Minor Arcs
A minor arc is a fundamental concept in geometry, representing a specific segment of a circle's circumference. It is defined as the shorter path along the circle's edge between two given points.
- Definition: A minor arc is a portion of a circle's circumference that subtends an angle less than 180 degrees at the center of the circle.
- Central Angle Connection: The measure of a minor arc is directly equal to the measure of its central angle. A central angle is formed when its vertex is at the exact center of the circle, and its sides are radii that extend to the endpoints of the arc on the circumference. For example, if the central angle is 75 degrees, the minor arc it defines also measures 75 degrees.
Minor Arc vs. Major Arc
To fully grasp the concept of a minor arc, it's helpful to understand how it contrasts with a major arc, which is the other primary type of arc in a circle.
| Feature | Minor Arc | Major Arc |
|---|---|---|
| Measure | Less than 180 degrees | Greater than 180 degrees |
| Size | Represents the "small" part of the arc | Represents the "large" part of the arc |
| Relation | Equal to its central angle | (360° - minor arc measure) |
| Path | The shorter path between two points | The longer path between the same two points |
Identifying and Measuring Minor Arcs
Identifying and measuring minor arcs is a common task in geometry:
- Identification: Given any two distinct points on a circle, there are always two arcs connecting them. The shorter of these two arcs is the minor arc.
- Measurement: The measure of a minor arc is identical to the measure of the central angle that "opens up" to the arc.
- For example, if you have a circle with a central angle of 120 degrees, the arc created by the two radii forming that angle is a minor arc measuring 120 degrees.
- Similarly, if a circle has a radius of 5 units and two points on its circumference form a 45-degree angle at the center, the arc connecting these two points is a minor arc of 45 degrees.
Minor arcs are essential for calculating arc lengths (the actual distance along the curve) and the areas of circular sectors, providing a foundational element for various geometric computations. For more information on circle components, refer to resources on Understanding Arcs and Central Angles.
